Abstract
We develop a formalism for computing inclusive production cross sections of heavy quarkonia based on the nonrelativistic QCD and the potential nonrelativistic QCD effective field theories. Our formalism applies to strongly coupled quarkonia, which include excited charmonium and bottomonium states. Analogously to heavy quarkonium decay processes, we express nonrelativistic QCD long-distance matrix elements in terms of quarkonium wavefunctions at the origin and universal gluonic correlators. Our expressions for the long-distance matrix elements are valid up to corrections of order 1/{N}_c^2 . These expressions enhance the predictive power of the nonrelativistic effective field theory approach to inclusive production processes by reducing the number of nonperturbative unknowns, and make possible first-principle determinations of long-distance matrix elements once the gluonic correlators are known. Based on this formalism, we compute the production cross sections of P-wave charmonia and bottomonia at the LHC, and find good agreement with measurements.
Highlights
Based constraints, or even computations, of the NRQCD LDMEs, in order to enhance significantly our understanding of the heavy quarkonium production mechanism
We develop a formalism for computing inclusive production cross sections of heavy quarkonia based on the nonrelativistic QCD and the potential nonrelativistic QCD effective field theories
The LDMEs that appear in the NRQCD factorization formulas for inclusive production cross sections of heavy quarkonia describe the evolution of a heavy quark and antiquark pair into a heavy quarkonium state
Summary
In the NRQCD factorization formalism, the inclusive production cross section of a quarkonium Q is given by [5]. If the effect of dynamical light quarks is neglected (the coupling of light mesons to quarkonia below threshold is a subleading effect, suppressed by powers of momenta of the light mesons, which is of order mv2), the dynamical degrees of freedom of pNRQCD consist of quarkonia and quarkonium exotica [14, 15, 17] These degrees of freedom are represented by fields Sn annihilating a color-singlet heavy quark-antiquark pair with light degrees of freedom in a state n. If we assume the simplest scenario that the energy levels for different n are separated by a gap of order ΛQCD, or that the mixing between fields with different n may be neglected, we can isolate the dynamics of one single field Sn. The strongly coupled pNRQCD Hamiltonian that describes this dynamics is HpNRQCD = d3x1 d3x2 Sn† hn(x1, x2; ∇1, ∇2) Sn. The function hn(x1, x2; ∇1, ∇2)δ(3)(x1 − x1)δ(3)(x2 − x2) is determined by matching to the NRQCD matrix element n; x1, x2|HNRQCD |n; x1, x2 of eq (2.10). This leads to the pNRQCD expression for the operator PQ(P =0):
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